Our results on the observables \(K^{\rm loc,h}(\hat{E},j)\) , the total circular peristron advance \(K^{\rm tot}(j)\) , the
circular binding energy \(E^{\rm circ}\)  and the contributions to the scattering angle \(\chi _k,~~k \in [1,6]\) , do agree
with the results of Ref. [1]}, in the case of the parameters given there,
except of the rational \(O(\nu ^2)\)  term of \(q_{44}\) . Furthermore, we have also newly obtained
the rational contributions of \(O(\nu ^2)\)  to \(\bar{d}_5\)  and \(a_6\)  for the first time. The \(O(\nu ^2 \pi ^2)\) 
contributions to
\(q_{44}\)  were obtained in [2]} and those to \(\bar{d}_5\)  and \(a_6\)  in [3]} before.
These terms
stem from the potential contributions. For them the relation (REF ) holds. Our calculation of the 5PN Hamiltonian ab
initio leads to a violation of relation (REF ) for the \(O(\nu ^2)\)  rational term in \(q_{44}\) . As has been outlined in
Section , the results of [2]} could be obtained by envoking the additional term
(REF , REF ) changing only \(q_{44}\) , but leaving \(\bar{d}_5\)  and \(a_6\)  invariant.
We presented numerical results to 5PN for \(E^{\rm circ}\)  and \(K^{\rm circ}\) .
